9.7 COSMO-MP2

In TURBOMOLE MP2 can be combined in two ways with the COSMO solvation model, which are known in the literature as “Perturbation Theory on Energy” (PTE) and “Perturbation Theory on Energy and Density” (PTED) approaches. The PTE approach is obtained by truncating the free energy of the solute strictly at second-order in the difference between the Hartree-Fock mean field and the Full Configuration Interaction electron-electron interaction, where the solvent-mediated electron-electron interaction is treated at the same footing as the direct electron-electron interaction. In the PTED approach the polarizable environment is self-consistently equilibrated with the correlated MP2 density. Thereby some higher-order contributions are included. These higher-order terms should be small since the supposition underlying MP2 is that the difference between the Hartree-Fock and the MP2 wavefunction should be small — if this is not fulfilled, MP2 is not adequate.

The PTE-COSMO-MP2 energy is obtained by adding to the COSMO-HF free energy the MP2 correlation energy evaluated with the MOs and the Fock matrix from a COSMO-HF calculation. The PTE-COSMO-MP2 approach is implemented in mpgrad for energies and in ricc2 for energies, first-order properties and gradients with closed-shell RHF or UHF reference wavefunctions. In ricc2 PTE-COSMO-MP2 calculations can be combined with spin-component scaling (SCS or SOS) and for SOS with the \({\cal O}({\cal N}^4)\)-scaling LT-based implementation.

Current restrictions for PTE-COSMO-MP2 are:

• Not available for ROHF reference wavefunctions

• Not available for second-order properties (polarizabilities)

• Not available for vibrational frequencies (see Sec. 21.2 for the complications that arise for the calculation of vibrational frequencies in solution)

The PTED approach is implemented in both mpgrad and ricc2 for energies. PTED-COSMO-MP2 gradients are only available in ricc2, see Sec. 10.9 for details.

PTE-COSMO-MP2 gradients require in addition to the input needed for MP2 gradients only the input for the $cosmo data group, no further additional options. The geometry optimization can be done with jobex as in the vacuum case. A PTED-COSMO-RI-MP2 geometry optimization with ricc2 using the Gaussian Charge Model (GCM) for COSMO and water as solvent can be done with the following input:

$ricc2
 geoopt model=mp2
$cosmo
  solvent=water
  gauss